arXiv subjects

Ullrich Köthe

Publications and source records attributed to Ullrich Köthe.

At least 55 records · Page 3Linked to original sources

arXiv2022

Towards Multimodal Depth Estimation from Light Fields

Light field applications, especially light field rendering and depth estimation, developed rapidly in recent years. While state-of-the-art light field rendering methods handle semi-transparent and reflective objects well, depth estimation methods either ignore these cases altogether or only deliver a weak performance. We argue that this is due current methods only considering a single "true" depth, even when multiple objects at different depths contributed to the color of a single pixel. Based on the simple idea of outputting a posterior depth distribution instead of only a single estimate, we develop and explore several different deep-learning-based approaches to the problem. Additionally, we contribute the first "multimodal light field depth dataset" that contains the depths of all objects which contribute to the color of a pixel. This allows us to supervise the multimodal depth prediction and also validate all methods by measuring the KL divergence of the predicted posteriors. With our thorough analysis and novel dataset, we aim to start a new line of depth estimation research that overcomes some of the long-standing limitations of this field.

cs.CV↗

arXiv2021

OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany

Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and intervention measures during an ongoing outbreak. However, reliably inferring the dynamics of ongoing outbreaks by connecting complex models to real data is still hard and requires either laborious manual parameter fitting or expensive optimization methods which have to be repeated from scratch for every application of a given model. In this work, we address this problem with a novel combination of epidemiological modeling with specialized neural networks. Our approach entails two computational phases: In an initial training phase, a mathematical model describing the epidemic is used as a coach for a neural network, which acquires global knowledge about the full range of possible disease dynamics. In the subsequent inference phase, the trained neural network processes the observed data of an actual outbreak and infers the parameters of the model in order to realistically reproduce the observed dynamics and reliably predict future progression. With its flexible framework, our simulation-based approach is applicable to a variety of epidemiological models. Moreover, since our method is fully Bayesian, it is designed to incorporate all available prior knowledge about plausible parameter values and returns complete joint posterior distributions over these parameters. Application of our method to the early Covid-19 outbreak phase in Germany demonstrates that we are able to obtain reliable probabilistic estimates for important disease characteristics, such as generation time, fraction of undetected infections, likelihood of transmission before symptom onset, and reporting delays using a very moderate amount of real-world observations.

stat.AP↗

arXiv2021

Inference of cosmic-ray source properties by conditional invertible neural networks

The inference of physical parameters from measured distributions constitutes a core task in physics data analyses. Among recent deep learning methods, so-called conditional invertible neural networks provide an elegant approach owing to their probability-preserving bijective mapping properties. They enable training the parameter-observation correspondence in one mapping direction and evaluating the parameter posterior distributions in the reverse direction. Here, we study the inference of cosmic-ray source properties from cosmic-ray observations on Earth using extensive astrophysical simulations. We compare the performance of conditional invertible neural networks (cINNs) with the frequently used Markov Chain Monte Carlo (MCMC) method. While cINNs are trained to directly predict the parameters' posterior distributions, the MCMC method extracts the posterior distributions through a likelihood function that matches simulations with observations. Overall, we find good agreement between the physics parameters derived by the two different methods. As a result of its computational efficiency, the cINN method allows for a swift assessment of inference quality.

astro-ph.IM↗

arXiv2021

Benchmarking Invertible Architectures on Inverse Problems

Recent work demonstrated that flow-based invertible neural networks are promising tools for solving ambiguous inverse problems. Following up on this, we investigate how ten invertible architectures and related models fare on two intuitive, low-dimensional benchmark problems, obtaining the best results with coupling layers and simple autoencoders. We hope that our initial efforts inspire other researchers to evaluate their invertible architectures in the same setting and put forth additional benchmarks, so our evaluation may eventually grow into an official community challenge.

cs.LG↗

arXiv2021

HINT: Hierarchical Invertible Neural Transport for Density Estimation and Bayesian Inference

Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation is invertible, its Jacobian is very sparse and thus may lack expressiveness. This work presents a simple remedy by noting that subdivision and (affine) coupling can be repeated recursively within the resulting subsets, leading to an efficiently invertible block with dense, triangular Jacobian. By formulating our recursive coupling scheme via a hierarchical architecture, HINT allows sampling from a joint distribution p(y,x) and the corresponding posterior p(x|y) using a single invertible network. We evaluate our method on some standard data sets and benchmark its full power for density estimation and Bayesian inference on a novel data set of 2D shapes in Fourier parameterization, which enables consistent visualization of samples for different dimensionalities.

stat.ML↗

arXiv2021

Conditional Invertible Neural Networks for Diverse Image-to-Image Translation

We introduce a new architecture called a conditional invertible neural network (cINN), and use it to address the task of diverse image-to-image translation for natural images. This is not easily possible with existing INN models due to some fundamental limitations. The cINN combines the purely generative INN model with an unconstrained feed-forward network, which efficiently preprocesses the conditioning image into maximally informative features. All parameters of a cINN are jointly optimized with a stable, maximum likelihood-based training procedure. Even though INN-based models have received far less attention in the literature than GANs, they have been shown to have some remarkable properties absent in GANs, e.g. apparent immunity to mode collapse. We find that our cINNs leverage these properties for image-to-image translation, demonstrated on day to night translation and image colorization. Furthermore, we take advantage of our bidirectional cINN architecture to explore and manipulate emergent properties of the latent space, such as changing the image style in an intuitive way.

cs.CV↗

arXiv2021

The Mutex Watershed and its Objective: Efficient, Parameter-Free Graph Partitioning

Image partitioning, or segmentation without semantics, is the task of decomposing an image into distinct segments, or equivalently to detect closed contours. Most prior work either requires seeds, one per segment; or a threshold; or formulates the task as multicut / correlation clustering, an NP-hard problem. Here, we propose an efficient algorithm for graph partitioning, the "Mutex Watershed''. Unlike seeded watershed, the algorithm can accommodate not only attractive but also repulsive cues, allowing it to find a previously unspecified number of segments without the need for explicit seeds or a tunable threshold. We also prove that this simple algorithm solves to global optimality an objective function that is intimately related to the multicut / correlation clustering integer linear programming formulation. The algorithm is deterministic, very simple to implement, and has empirically linearithmic complexity. When presented with short-range attractive and long-range repulsive cues from a deep neural network, the Mutex Watershed gives the best results currently known for the competitive ISBI 2012 EM segmentation benchmark.

cs.CV↗

arXiv2021

Measuring QCD Splittings with Invertible Networks

QCD splittings are among the most fundamental theory concepts at the LHC. We show how they can be studied systematically with the help of invertible neural networks. These networks work with sub-jet information to extract fundamental parameters from jet samples. Our approach expands the LEP measurements of QCD Casimirs to a systematic test of QCD properties based on low-level jet observables. Starting with an toy example we study the effect of the full shower, hadronization, and detector effects in detail.

hep-ph↗

arXiv2021

Amortized Bayesian model comparison with evidential deep learning

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for guiding decisions. However, many interesting models are intractable with standard Bayesian methods, as they lack a closed-form likelihood function or the likelihood is computationally too expensive to evaluate. With this work, we propose a novel method for performing Bayesian model comparison using specialized deep learning architectures. Our method is purely simulation-based and circumvents the step of explicitly fitting all alternative models under consideration to each observed dataset. Moreover, it requires no hand-crafted summary statistics of the data and is designed to amortize the cost of simulation over multiple models and observable datasets. This makes the method particularly effective in scenarios where model fit needs to be assessed for a large number of datasets, so that per-dataset inference is practically infeasible.Finally, we propose a novel way to measure epistemic uncertainty in model comparison problems. We demonstrate the utility of our method on toy examples and simulated data from non-trivial models from cognitive science and single-cell neuroscience. We show that our method achieves excellent results in terms of accuracy, calibration, and efficiency across the examples considered in this work. We argue that our framework can enhance and enrich model-based analysis and inference in many fields dealing with computational models of natural processes. We further argue that the proposed measure of epistemic uncertainty provides a unique proxy to quantify absolute evidence even in a framework which assumes that the true data-generating model is within a finite set of candidate models.

stat.ML↗

arXiv2021

Learning Robust Models Using The Principle of Independent Causal Mechanisms

Standard supervised learning breaks down under data distribution shift. However, the principle of independent causal mechanisms (ICM, Peters et al. (2017)) can turn this weakness into an opportunity: one can take advantage of distribution shift between different environments during training in order to obtain more robust models. We propose a new gradient-based learning framework whose objective function is derived from the ICM principle. We show theoretically and experimentally that neural networks trained in this framework focus on relations remaining invariant across environments and ignore unstable ones. Moreover, we prove that the recovered stable relations correspond to the true causal mechanisms under certain conditions. In both regression and classification, the resulting models generalize well to unseen scenarios where traditionally trained models fail.

cs.LG↗

arXiv2021

Training Normalizing Flows with the Information Bottleneck for Competitive Generative Classification

The Information Bottleneck (IB) objective uses information theory to formulate a task-performance versus robustness trade-off. It has been successfully applied in the standard discriminative classification setting. We pose the question whether the IB can also be used to train generative likelihood models such as normalizing flows. Since normalizing flows use invertible network architectures (INNs), they are information-preserving by construction. This seems contradictory to the idea of a bottleneck. In this work, firstly, we develop the theory and methodology of IB-INNs, a class of conditional normalizing flows where INNs are trained using the IB objective: Introducing a small amount of {\em controlled} information loss allows for an asymptotically exact formulation of the IB, while keeping the INN's generative capabilities intact. Secondly, we investigate the properties of these models experimentally, specifically used as generative classifiers. This model class offers advantages such as improved uncertainty quantification and out-of-distribution detection, but traditional generative classifier solutions suffer considerably in classification accuracy. We find the trade-off parameter in the IB controls a mix of generative capabilities and accuracy close to standard classifiers. Empirically, our uncertainty estimates in this mixed regime compare favourably to conventional generative and discriminative classifiers.

cs.LG↗

arXiv2020

Generative Classifiers as a Basis for Trustworthy Image Classification

With the maturing of deep learning systems, trustworthiness is becoming increasingly important for model assessment. We understand trustworthiness as the combination of explainability and robustness. Generative classifiers (GCs) are a promising class of models that are said to naturally accomplish these qualities. However, this has mostly been demonstrated on simple datasets such as MNIST and CIFAR in the past. In this work, we firstly develop an architecture and training scheme that allows GCs to operate on a more relevant level of complexity for practical computer vision, namely the ImageNet challenge. Secondly, we demonstrate the immense potential of GCs for trustworthy image classification. Explainability and some aspects of robustness are vastly improved compared to feed-forward models, even when the GCs are just applied naively. While not all trustworthiness problems are solved completely, we observe that GCs are a highly promising basis for further algorithms and modifications. We release our trained model for download in the hope that it serves as a starting point for other generative classification tasks, in much the same way as pretrained ResNet architectures do for discriminative classification.

cs.CV↗

arXiv2020

BayesFlow: Learning complex stochastic models with invertible neural networks

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit likelihood function is not available. With this work, we propose a novel method for globally amortized Bayesian inference based on invertible neural networks which we call BayesFlow. The method uses simulation to learn a global estimator for the probabilistic mapping from observed data to underlying model parameters. A neural network pre-trained in this way can then, without additional training or optimization, infer full posteriors on arbitrary many real datasets involving the same model family. In addition, our method incorporates a summary network trained to embed the observed data into maximally informative summary statistics. Learning summary statistics from data makes the method applicable to modeling scenarios where standard inference techniques with hand-crafted summary statistics fail. We demonstrate the utility of BayesFlow on challenging intractable models from population dynamics, epidemiology, cognitive science and ecology. We argue that BayesFlow provides a general framework for building amortized Bayesian parameter estimation machines for any forward model from which data can be simulated.

stat.ML↗

arXiv2020

Invertible Neural Networks for Uncertainty Quantification in Photoacoustic Imaging

Multispectral photoacoustic imaging (PAI) is an emerging imaging modality which enables the recovery of functional tissue parameters such as blood oxygenation. However, the underlying inverse problems are potentially ill-posed, meaning that radically different tissue properties may - in theory - yield comparable measurements. In this work, we present a new approach for handling this specific type of uncertainty by leveraging the concept of conditional invertible neural networks (cINNs). Specifically, we propose going beyond commonly used point estimates for tissue oxygenation and converting single-pixel initial pressure spectra to the full posterior probability density. This way, the inherent ambiguity of a problem can be encoded with multiple modes in the output. Based on the presented architecture, we demonstrate two use cases which leverage this information to not only detect and quantify but also to compensate for uncertainties: (1) photoacoustic device design and (2) optimization of photoacoustic image acquisition. Our in silico studies demonstrate the potential of the proposed methodology to become an important building block for uncertainty-aware reconstruction of physiological parameters with PAI.

physics.med-ph↗

arXiv2020

Invertible Networks or Partons to Detector and Back Again

For simulations where the forward and the inverse directions have a physics meaning, invertible neural networks are especially useful. A conditional INN can invert a detector simulation in terms of high-level observables, specifically for ZW production at the LHC. It allows for a per-event statistical interpretation. Next, we allow for a variable number of QCD jets. We unfold detector effects and QCD radiation to a pre-defined hard process, again with a per-event probabilistic interpretation over parton-level phase space.

hep-ph↗

arXiv2020

Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)

A central question of representation learning asks under which conditions it is possible to reconstruct the true latent variables of an arbitrarily complex generative process. Recent breakthrough work by Khemakhem et al. (2019) on nonlinear ICA has answered this question for a broad class of conditional generative processes. We extend this important result in a direction relevant for application to real-world data. First, we generalize the theory to the case of unknown intrinsic problem dimension and prove that in some special (but not very restrictive) cases, informative latent variables will be automatically separated from noise by an estimating model. Furthermore, the recovered informative latent variables will be in one-to-one correspondence with the true latent variables of the generating process, up to a trivial component-wise transformation. Second, we introduce a modification of the RealNVP invertible neural network architecture (Dinh et al. (2016)) which is particularly suitable for this type of problem: the General Incompressible-flow Network (GIN). Experiments on artificial data and EMNIST demonstrate that theoretical predictions are indeed verified in practice. In particular, we provide a detailed set of exactly 22 informative latent variables extracted from EMNIST.

cs.LG↗

arXiv2019

Out of distribution detection for intra-operative functional imaging

Multispectral optical imaging is becoming a key tool in the operating room. Recent research has shown that machine learning algorithms can be used to convert pixel-wise reflectance measurements to tissue parameters, such as oxygenation. However, the accuracy of these algorithms can only be guaranteed if the spectra acquired during surgery match the ones seen during training. It is therefore of great interest to detect so-called out of distribution (OoD) spectra to prevent the algorithm from presenting spurious results. In this paper we present an information theory based approach to OoD detection based on the widely applicable information criterion (WAIC). Our work builds upon recent methodology related to invertible neural networks (INN). Specifically, we make use of an ensemble of INNs as we need their tractable Jacobians in order to compute the WAIC. Comprehensive experiments with in silico, and in vivo multispectral imaging data indicate that our approach is well-suited for OoD detection. Our method could thus be an important step towards reliable functional imaging in the operating room.

eess.IV↗

arXiv2019

Object Segmentation using Pixel-wise Adversarial Loss

Recent deep learning based approaches have shown remarkable success on object segmentation tasks. However, there is still room for further improvement. Inspired by generative adversarial networks, we present a generic end-to-end adversarial approach, which can be combined with a wide range of existing semantic segmentation networks to improve their segmentation performance. The key element of our method is to replace the commonly used binary adversarial loss with a high resolution pixel-wise loss. In addition, we train our generator employing stochastic weight averaging fashion, which further enhances the predicted output label maps leading to state-of-the-art results. We show, that this combination of pixel-wise adversarial training and weight averaging leads to significant and consistent gains in segmentation performance, compared to the baseline models.

cs.CV↗